Bring 3 cups of water to a boil in a medium pot. Whisk in the polenta and reduce the heat to medium-low. Stir the polenta often as it thickens. Reduce the heat to low and continue to cook, stirring occasionally, until the polenta is thick and the corn flavor has mellowed; 25 to 30 minutes. Remove from the heat and stir in the butter/salt.

While the polenta is cooking, place the dill on a cutting board. Add the lemon zest and salt on top. Roughly mince everything together, chopping into a cohesive mix. Add the toasted pistachios and continue to chop until the nuts are in small pieces and are well coated with the dill mix.

Heat a large skillet over medium-high heat. Trim the ends from the asparagus and cut the stalks into bite-sized pieces. Add the ghee to the heated pan, melt, then add the asparagus to the pan. Cook until the asparagus is charred, bright green in color, and still slightly crisp in texture. Remove from heat and toss with ¾ of the dill mixture.

Divide the polenta into 3 to 4 bowls. Top with a spoonful of burrata and the asparagus mixture. Finish with a sprinkle of the dill mixture before serving.